We define two classes of rings calling them weakly clean rings and weakly exchange rings both equipped with the strong property. Although the classes of weakly clean rings and weakly exchange rings are different, their two proper subclasses above do coincide. This extends results due to W. Chen (Commun. Algebra, 2006) and Chin-Qua (Acta Math. Hungar., 2011). We also completely characterize stro...

The aim of this study is to provide a generalization prime vague Γ-ideals in Γ-rings by introducing non-symmetric 2-absorbing weakly complete commutative Γ-rings. A novel algebraic structure primary Γ-ideal Γ-ring presented ideal theory. approach K-vague are examined and the relation between level subset given. image inverse studied 1-1 inclusion-preserving correspondence theorem quotient R ind...

Let G be a group and R G-graded ring. In this paper, we present examine the concept of graded weakly 2-absorbing ideals as in generality prime ring which is not commutative, demonstrates that symmetry obtained lot outcomes commutative rings remain are commutative.